Contents
1 Introduction
1.1 Types of Time Series
1.2 Objectives of Time Series
1.3 Descriptive Techniques
1.4 Stationary Time Series
1.5 Transformation
1.6 Auto correlation
2 Stochastic Process
2.1 Second Order Stationary
3 Random Process
4 Random Walk
5 Moving Average (Ma)
6 Invertibility
7 Autoregressive Process
7.1 General Order Of an AR Process
8 Mixed Arma Models
9 Integrated Arma
10 Forecasting
10.1 The Partial Autocorrelation Function
11 Estimation Of Models
11.1 Fitting an AR Model
11.2 Fitting an MA Process
11.3 Box-Jenkins Seasonal (SARIMA) Model
11.4 Forecasting: (Box-Jenkins Procedure)
11.5 Computation of Forecast
12 The Frequency Domain
12.1 The Spectral Density
12.2 The Periodogram
13 State Space Models And The Kalman Filter
13.1 The Linear Model
13.2 The Kalman Filter
14 Nonlinear Models: ARCH And Volatility
15 Practice Problems
1.1 Types of Time Series
1.2 Objectives of Time Series
1.3 Descriptive Techniques
1.4 Stationary Time Series
1.5 Transformation
1.6 Auto correlation
2 Stochastic Process
2.1 Second Order Stationary
3 Random Process
4 Random Walk
5 Moving Average (Ma)
6 Invertibility
7 Autoregressive Process
7.1 General Order Of an AR Process
8 Mixed Arma Models
9 Integrated Arma
10 Forecasting
10.1 The Partial Autocorrelation Function
11 Estimation Of Models
11.1 Fitting an AR Model
11.2 Fitting an MA Process
11.3 Box-Jenkins Seasonal (SARIMA) Model
11.4 Forecasting: (Box-Jenkins Procedure)
11.5 Computation of Forecast
12 The Frequency Domain
12.1 The Spectral Density
12.2 The Periodogram
13 State Space Models And The Kalman Filter
13.1 The Linear Model
13.2 The Kalman Filter
14 Nonlinear Models: ARCH And Volatility
15 Practice Problems
TIME SERIES ANALYSIS
August 24, 2026
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\(Def^n\):
A time series is an ordered sequence of observations.
The ordering is usually in time or other dimensions e.g space.
APPLICATION OF TIME SERIES
- 1.
- Agriculture
- (a)
- Observation of annual crops production
- (b)
- Annual livestock
- (c)
- Prices of crops over time
- 2.
- Business and Economics
- (a)
- Annual sales of a product
- (b)
- Price of commodity
- (c)
- Price induces (inflation e.t.c)
- (d)
- Annual earnings at a stock exchange market
- (e)
- Exchange rate
- 3.
- Engineering
- (a)
- Electrical signals
- (b)
- Voltage
- (c)
- Sound monitoring
- 4.
- Geophysics
- (a)
- turbulence of waves (ocean)
- 5.
- Meteorology
- (a)
- Sea surface temperatures
- (b)
- Wind speed
- 6.
- Medical Studies
- (a)
- Mortality rate (Annual)
- (b)
- Failure rate of surgery
- 7.
- Quality Control
- (a)
- Monitor a production process
- 8.
- Social Sciences
- (a)
- Annual birthrate
- (b)
- Mortality rate
- (c)
- Accident rates
- (d)
- Crime rates